Chap. 6 Multiphase Systems
All chemical processes involve multiphase operations:
- Phase-change operations: freezing, melting, evaporation, condensation
- Separation and purification processes: leaching, absorption, distillation,
extraction, adsorption, crystallization, …
(Examples)
1. Brewing a cup of coffee - leaching(침출)
2. Removal of sulfur dioxide from a gas stream - absorption(흡수)
S  SO2  in the air SO3  H2SO4(acid rain)
3. Recovery of methanol from an aqueous solution - distillation
4. Separation of paraffinic and aromatic hydrocarbons - liquid extraction(추출)
5. Separation of an isomeric mixture - adsorption(흡착), crystallization
-Molecular sieve
6. Concentrate O2 for breathing –impaired patients - adsorption
7. Obtain fresh water from seawater-evaporation, reverse osmosis
Driving force in the separation processes  concentration difference  phase
equilibrium
6.1 SINGLE –COMPONENT PHASE EQUILIBRIUM
6.1a Phase Diagram
A phase diagram of a pure substance is a plot of one system variable
against another ( mostly PT diagram ) that shows the conditions at which
the substance exists as a solid, a liquid, and a gas.
PT diagram
vapor-liquid equilibrium: boiling point/vapor pressure
solid-liquid equilibrium: melting point(freezing point)
solid-vapor equilibrium: sublimation point
triple point
critical point: critical temperature/critical pressure
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*Freezing point of water decreases with increasing pressure:
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*Molecular crystals: many small, discrete, covalently bonded
molecules by van der Vaals or hydrogen bonding
CO2: FCC
Methane(below -183C): FCC
H2O(Ih at atmospheric pressure): HCP
Many organic compounds: energetic materials, …..
CO2
H2O
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6.1b Estimation of Vapor Pressure
The volatility of a species: the degree to which the species tends to transfer
from the liquid state to the vapor state
The vapor pressure of a species: a measure of its volatility
Often vapor pressure data are not available at temperatures of interest.
- Measure the vapor pressure at the desired temperature
-
Estimate the vapor pressure using an empirical correlation
Clapeyron equation: relationship between the vapor pressure of a pure
substance ( p * ) and the absolute temperature ( T )
Hˆ v
dp*

dT T Vˆg  Vˆl


(6.1-1)
Where Vˆg , Vˆl : vapor와 liquid의 specific molar volume
Hˆ v : Latent heat of vaporization
When pressure is not extremely high: Vˆg Vˆl , Vˆg  Vˆl  Vˆg
The vapor is assumed to be ideal gas: Vˆg 
RT
p*
Hˆ v
dp *

dT T  RT
p*
dp* Hˆ v dT


p*
R T2


d ln p* 


Hˆ v
R
  1 
   d   
  T 
Hˆ v
d ln p *

1
R
d( )
T
(6.1-2)
commonly used to determine heats of vaporization experimentally.
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Clausius-Clapeyron equation: Suppose that the heat of vaporization of a
substance ( Hˆ v ) is independent of temperature,
ln p*  
Plot of
Hˆ v
B
RT
ln p* vs.
(6.1-3)
Hˆ v
1
should be straight line with slope
and intercept B .
T
R
Antoine equation: an empirical
temperature data extremely well.
log10 p*  A 
equation
correlates
vapor
pressure-
B
T C
( p* : mmHg, T :C , constants A,B,C: Table B.4 )
Vapor pressure vs. temperature
Duhring plots
Cox chart (Figure 6.1-4)
Ex. 6.1-1) vapor pressure estimation using the Clausius-Clapeyron Equation
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6.2 THE GIBBS PHASE RULE
Extensive variable(크기변수): depend on the system size(mass, volume, …)
Intensive variable(세기변수): temperature, pressure, density, …
degree of freedom(자유도, DF) : the number of intensive variables that can be
specified for a system at equilibrium.
Gibbs phase rule
DF  2  c   ,
where

c
: number of phase
: number of species
Ex. 6.2-1 The Gibbs Phase Rule
Josiah Willard Gibbs (February 11, 1839 – April 28, 1903): an American
theoretical physicist, chemist, and mathematician. He devised much of the
theoretical foundation for chemical thermodynamics as well as physical
chemistry. As a mathematician, he invented vector analysis (independently of
Oliver Heaviside). Yale University awarded Gibbs the first American Ph.D. in
engineering in 1863, and he spent his entire career at Yale.
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6.3 GAS-LIQUID SYSTEMS: ONE CONDENSABLE COMPONENT
Saturation: the gas phase contains all the vapor of a condensable species it
can hold at the system temperature and pressure.
In an air-water system: humidity
Raoult’s law, single condensable species: pi  yi P  pi* (T )
Superheated vapor: a vapor resent in a gas in less than its saturation amount:
pi  yi P  pi* (T )
Dew point: if a gas containing a single superheated vapor is cooled at constant
pressure, the temperature at which the vapor becomes saturated:
pi  yi P  pi* Tdp 
Degree of superheat of the gas: the difference between the temperature and
the dew point
Boiling point of the liquid at the given temperature: the temperature at which
p*  P
Relative saturation (relative humidity) :
p
s r (hr )  *i  100%
pi
Molal saturation (molal humidity):
pi
moles of vapor
s m (hm ) 

P  pi moles of vaporfree(dry) gas
Absolute saturation (absolute humidity):
pi M i
mass of vapor
s a (ha ) 

P  pi M dry mass of dry gas
Percentage saturation (percentage humidity):
s
p / P  p i 
s p h p  m *  100%  *i
 100%
pi / P  pi*
sm 


Ex. 6.3-1) composition of a saturated gas-vapor system
Ex) 6.3-2) Material Balances around a Condenser
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6.4 MULTICOMPONENT GAS-LIQUID SYSTEMS
6.4a Vapor-Liquid Equilibrium data
6.4b Raoult’s law and Henry’s law
Raoult’s law: p A  y A P  x A p *A (T ) : Generally valid when x A is close to 1.
Henry’s law: p A  y A P  x A H A (T ) : H A (T ) is the Henry’s constant. Generally
valid when x A is close to 0 provide that A does not dissociate, ionize, or react in
the liquid phase.
Ideal solution:
Ex.6.4-2) Raoult’s Law and Henry’s Law
6.4c Vapor-Liquid Equilibrium Calculations for Ideal Solutions
bubble point: the temperature at which first bubble forms when a liquid is
heated slowly at constant pressure.
dew point: the temperature at which the first liquid droplet forms when a vapor
is cooled slowly at constant pressure.
Suppose an Ideal solution follows Raoult’s law and contains species A, B, C,
… If the mixture is heated at constant pressure P to its bubble-point temp.,
Tbp , the further addition of a slight amount of heat will lead to the formation of a
vapor phase. The partial pressures of the components are given by Raoult’s law.
pi  xi pi* Tbp  ,
i  A, B, C,
P   pi   xi pi* Tbp 
Tbp may be calculated by trial and error. pi* T  can be obtained by Antoine
equation or tables.
Bubble point pressure: the pressure at which the first vapor forms when a
liquid is decompressed at a constant temperature. The mole fraction in the
vapor in equilibrium with the liquid (ideal liquid) is
yi 
pi
x p * (T )
 i i
Pbp
Pbp
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Suppose a gas phase contains the condensable components A, B, C, … and a
noncondensable component G at a fixed pressure P. If the gas mixture is
cooled slowly to its dew point, it will be in equilibrium with the first liquid that
forms. Assuming that Raoult’s law applies, the liquid phase mole fractions
are:
xi 
yi P
, i  A, B, C ,excludingG
p (Tdp )
*
i
x   p
i
yi P
(Tdp )
*
i
1
Dew point pressure: the pressure at which the first liquid droplet forms when a
vapor is compressed at a constant temperature
Pdp 
1
p
yi
(T )
*
i
Ex. 6.4-3) Bubble and dew-point calculations
6.4d Graphical Representation of Vapor-Liquid Equilibrium
Figure 6.4-1
Boiling: a specific type of vaporization process in which vapor bubbles form at
a heated surface and escape from the liquid.
Vaporization: molecular evaporation of liquid from a gas-liquid interface, which
may occur at temperatures below the boiling point.
Ex. 6.4-4) Bubble and Dew-point Calculations using Txy Diagrams
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6.5 SOLUTIONS OF SOLIDS IN LIQUIDS
6.5a Solubility and Saturation
Solubility of a solid in a liquid: the maximum amount of that substance which
can be dissolved in a specified amount of the liquid at equilibrium.
In general, g solute dissolved/100g solvent.
Saturated solution: A solution
that contains as much of a
dissolved species as it can at
equilibrium
Supersaturation:
difference
between actual and equilibrium
concentrations.
Figure 6.5-1 Solubilities of inorganic solutes
Metastable zone width
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6.5b Solid Solubilities and Hydrate Salts
Polymorphism ( 다형(多形), 동질이형(同質異形), 동질다상(同質多像), 동질이
정(同質異晶) )
- Ability of any element or compound to crystallize into at least two different
crystalline structures, but they should be identical in the liquid or gaseous
state.
- The different structures are called polymorphs, polymorphic modifications.
- If the material is an element, polymorphs are called allotropes.
- Differences in
morphological appearance
do
not
necessary reflect
polymorphism.
-Molecular conformation and packing caused by various intermolecular
forces, hydrogen bonding, van der Waals forces, interactions with solvents and
additives, etc..
-Which polymorphic form of a compound is formed depends on the
preparation
and
crystallization
conditions:
method
of
synthesis,
temperature, pressure, solvent, cooling and heating rate, seed crystals,
etc.
Example 1) Ammonium Nitrate ( NH4NO3 )
Ind. Eng. Chem. Res. 49, 12632-12637, 2010
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6 polymorphs between - 200 and 125 C
I: Cubic, II: Tetragonal, III: Orthorhombic, IV: Orthorhombic, V: Tetragonal
Phase stabilized AN
Caked AN
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Pseudopolymorphism
Solvates (Hydrates) which form as the result of compound formation with the
solvent (water). Stoichiometric
*Clathrate 내포화합물·포접(包接)화합물: adductive crystallization, inclusion
compound (the host and the guest). Nonstoichiometric
Example ) Ind. Eng. Chem. Res., 40, 6111-6117, 2001
L-phenylalanine ( C6H5CH2CH(NH2)CO2H )
One of the essential amino acid
Pharmaceutical intermediate
Food intermediate-Aspartame (l-aspartylphenylalanine methyl ester)
(L-aspartic acid)
Monohydrate
Anhydrate
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6.5c Colligative Solution Properties
Colligative properties(결합특성, 총괄성): properties of a solution that depend
on the number of solute particles present but not on the chemical properties of
the solute: vapor pressure, freezing point, boiling point, osmotic pressure
Consider a solution in which the solute mole fraction is x and assume that the
solute is nonvolatile, nonreactive, and nondissociative and Raoult’s law
holds.
By Raoult’s law, effective solvent vapor pressure:
p 
*
s e
 ps  (1  x) ps*
Vapor pressure lowering: ps*  ps*  ( ps* ) e  ps*  (1  x) ps*  xp s*
The lowing of solvent vapor pressure has two important consequences. The
solvent in a solution at a given pressure boils at a higher temperature and
freezes at a lower temperature than does the pure solvent at the same pressure.
Relationship between concentration and both boiling point elevation and
freezing point depression (Proof: prob. 6.87)
Boiling point elevation: Tb  Tbs  Tb 0 
RTb20
x
Hˆ v
RTm20
x
Freezing point depression: Tm  Tm 0  Tms 
Hˆ m
ex) 6.5-4
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6.6 EQUILIBRIUM BETWEEN TWO LIQUID PHASES
6.6a Miscibility and Distribution Coefficients
Ex.6.6-1) extraction of acetone from water
Water/Chloroform-immiscible,
Water/Acetone-miscible,
Chloroform/Acetone-miscible
Water/acetone solution + chloroform  acetone/water + acetone/chloroform
distribution coefficient (partition ratio): K 
x A C phase
 1.72
x A W phase
6.6b Phase Diagram for Ternary Systems
Figure 6.6-1
Triangular phase
diagram for
water-acetoneMIBK (methyl
isobutyl ketone)
at 25C
(1941)
Region A: a single liquid, Region B: two phases/tie line
Point K: 15wt% water, 65%acetone, 20%MIBK
Point M: 55wt% water, 15% acetone, 30% MIBK
two phases: point L(85% water, 12%acetone, 3%MIBK)
point N (4%water, 20%acetone, 76%MIBK)
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6.7 ADSORPTION ON SOLID SURFACES
ADSORPTION: The surface of a solid represents a discontinuity of its
structure. The forces acting at the surface are unsaturated. Hence, when
the solid is exposed to a gas, the gas molecules will form bonds with it
and become attached. ADSORBENT /ADSORBATE
Industrial sorbents
Activated carbon: 320m2/g
Molecular Sieve Carbon
(carbon molecular sieve)
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Activated Alumina
Silica Gel
Zeolite
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Macropores: d > 500 Å (50nm)
Mesopores: 20 Å < d < 500 Å
Micropores: d < 20 Å
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ADSORPTION ISOTHERM: adsorbate equilibrium data on a specific
adsorbent are often taken at a specific temperature.
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DETERMINATION OF AN ISOTHERM: CCl4/activated carbon (p.275)
Langmuir isotherm: X i* 
aK L pi
1  K L pi
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